Combining Texts

All the ideas for 'fragments/reports', 'Unpublished Notebooks 1872-74' and 'Set Theory'

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64 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
Wisdom prevents us from being ruled by the moment [Nietzsche]
1. Philosophy / A. Wisdom / 2. Wise People
Unlike science, true wisdom involves good taste [Nietzsche]
1. Philosophy / A. Wisdom / 3. Wisdom Deflated
Suffering is the meaning of existence [Nietzsche]
1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
Philosophy ennobles the world, by producing an artistic conception of our knowledge [Nietzsche]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
The first aim of a philosopher is a life, not some works [Nietzsche]
You should only develop a philosophy if you are willing to live by it [Nietzsche]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / f. Philosophy as healing
Philosophy is pointless if it does not advocate, and live, a new way of life [Nietzsche]
1. Philosophy / D. Nature of Philosophy / 6. Hopes for Philosophy
Philosophy is more valuable than much of science, because of its beauty [Nietzsche]
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
It would better if there was no thought [Nietzsche]
Why do people want philosophers? [Nietzsche]
Philosophy is always secondary, because it cannot support a popular culture [Nietzsche]
1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
Kant has undermined our belief in metaphysics [Nietzsche]
1. Philosophy / G. Scientific Philosophy / 3. Scientism
If philosophy controls science, then it has to determine its scope, and its value [Nietzsche]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y))) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
Choice: ∀A ∃R (R well-orders A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
Set Existence: ∃x (x = x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
Constructibility: V = L (all sets are constructible) [Kunen]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Logic is just slavery to language [Nietzsche]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
Things get smaller without end [Anaxagoras]
7. Existence / A. Nature of Existence / 1. Nature of Existence
Nothing is created or destroyed; there is only mixing and separation [Anaxagoras]
7. Existence / A. Nature of Existence / 3. Being / f. Primary being
Anaxagoras's concept of supreme Mind has a simple First and a multiple One [Anaxagoras, by Plotinus]
7. Existence / C. Structure of Existence / 6. Fundamentals / a. Fundamental reality
Basic is the potentially perceptible, then comes the contrary qualities, and finally the 'elements' [Anaxagoras]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
If some sort of experience is at the root of matter, then human knowledge is close to its essence [Nietzsche]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
Belief matters more than knowledge, and only begins when knowledge ceases [Nietzsche]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / b. Direct realism
It always remains possible that the world just is the way it appears [Nietzsche]
12. Knowledge Sources / B. Perception / 1. Perception
Snow is not white, and doesn't even appear white, because it is made of black water [Anaxagoras, by Cicero]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
The senses are too feeble to determine the truth [Anaxagoras]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Our knowledge is illogical, because it rests on false identities between things [Nietzsche]
The most extreme scepticism is when you even give up logic [Nietzsche]
13. Knowledge Criteria / D. Scepticism / 2. Types of Scepticism
We reveal unreliability in the senses when we cannot discriminate a slow change of colour [Anaxagoras, by Sext.Empiricus]
14. Science / D. Explanation / 3. Best Explanation / b. Ultimate explanation
If we find a hypothesis that explains many things, we conclude that it explains everything [Nietzsche]
15. Nature of Minds / A. Nature of Mind / 1. Mind / a. Mind
Nous is unlimited, self-ruling and pure; it is the finest thing, with great discernment and strength [Anaxagoras]
15. Nature of Minds / A. Nature of Mind / 1. Mind / c. Features of mind
Mind is self-ruling, pure, ordering and ubiquitous [Anaxagoras, by Plato]
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
Our primary faculty is perception of structure, as when looking in a mirror [Nietzsche]
15. Nature of Minds / C. Capacities of Minds / 9. Perceiving Causation
We experience causation between willing and acting, and thereby explain conjunctions of changes [Nietzsche]
16. Persons / F. Free Will / 1. Nature of Free Will
Anaxagoras says mind remains pure, and so is not affected by what it changes [Anaxagoras, by Aristotle]
17. Mind and Body / A. Mind-Body Dualism / 8. Dualism of Mind Critique
It is just madness to think that the mind is supernatural (or even divine!) [Nietzsche]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
The shortest path to happiness is forgetfulness, the path of animals (but of little value) [Nietzsche]
23. Ethics / C. Virtue Theory / 3. Virtues / g. Contemplation
Anaxagoras said a person would choose to be born to contemplate the ordered heavens [Anaxagoras]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Education is contrary to human nature [Nietzsche]
25. Social Practice / E. Policies / 5. Education / d. Study of history
We should evaluate the past morally [Nietzsche]
25. Social Practice / F. Life Issues / 6. Animal Rights
Protest against vivisection - living things should not become objects of scientific investigation [Nietzsche]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / a. Final purpose
For Anaxagoras the Good Mind has no opposite, and causes all movement, for a higher reason [Anaxagoras, by Aristotle]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / a. Greek matter
Mind creates the world from a mixture of pure substances [Anaxagoras, by ]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
Anaxagoras said that the number of principles was infinite [Anaxagoras, by Aristotle]
The ultimate constituents of reality are the homoeomeries [Anaxagoras, by Vlastos]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / f. Ancient elements
Anaxagoreans regard the homoeomeries as elements, which compose earth, air, fire and water [Anaxagoras, by Aristotle]
26. Natural Theory / C. Causation / 1. Causation
Anaxagoras says mind produces order and causes everything [Anaxagoras, by Plato]
26. Natural Theory / C. Causation / 3. Final causes
We do not know the nature of one single causality [Nietzsche]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
Laws of nature are merely complex networks of relations [Nietzsche]
27. Natural Reality / G. Biology / 1. Biology
Germs contain microscopic organs, which become visible as they grow [Anaxagoras]
28. God / A. Divine Nature / 1. God
When things were unified, Mind set them in order [Anaxagoras]
Anaxagoras was the first to say that the universe is directed by an intelligence [Anaxagoras, by Cicero]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
Past, present and future, and the movements of the heavens, were arranged by Mind [Anaxagoras]
28. God / C. Attitudes to God / 5. Atheism
Anaxagoras was charged with impiety for calling the sun a lump of stone [Anaxagoras, by Plutarch]
Anaxagoras was the first recorded atheist [Anaxagoras, by Watson]
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
The Greeks lack a normative theology: each person has their own poetic view of things [Nietzsche]